2013 OASDI Trustees Report

Significant uncertainty surrounds the estimates under the intermediate assumptions, especially for a period as long as 75 years. This appendix presents a way to illustrate the uncertainty of these estimates. The stochastic projections supplement the traditional methods of examining such uncertainty.
The Trustees have traditionally shown estimates using the low-cost and high-cost sets of specified assumptions to illustrate the presence of uncertainty. These alternative estimates provide a range of possible outcomes for the projections. However, they do not provide an indication of the probability that actual future experience will be inside or outside this range. This appendix presents the results of a model, based on stochastic modeling techniques, that estimates a probability distribution of future outcomes of the financial status of the combined OASI and DI Trust Funds. This model, which was first included in the 2003 report, is subject to further development.
This appendix presents estimates of the probability that key measures of OASDI solvency will fall in certain ranges, based on 5,000 independent stochastic simulations. Each simulation allows the above variables to vary throughout the long-range period. The fluctuation of each variable over time is simulated using historical data and standard time-series techniques. Generally, each variable is modeled using an equation that: (a) captures a relationship between current and prior years’ values of the variable; and (b) introduces year-by-year random variation as observed in the historical period. For some variables, the equations also reflect relationships with other variables. The equations contain parameters that are estimated using historical data for periods between 25 years and 110 years, depending on the nature and quality of the available data. Each time-series equation is designed so that, in the absence of random variation over time, the value of the variable for each year equals its value under the intermediate assumptions.1
For each simulation, the stochastic method develops year-by-year random variation in most of the variables using Monte Carlo techniques. The one exception is that the model varies net other immigration directly rather than as the difference of its components (other immigration minus other emigration). Each simulation produces an estimate of the financial status of the combined OASI and DI Trust Funds. This appendix shows the distribution of results from 5,000 simulations of the model.
Readers should interpret the results from this model with caution and with an understanding of the model’s limitations. Results are very sensitive to equation specifications, degrees of interdependence among variables, and the historical periods used for the estimates. For some variables, recent historical variation may not provide a realistic representation of the potential variation for the future. Also, results would differ if additional variables (such as labor force participation rates, retirement rates, marriage rates, and divorce rates) were also allowed to vary randomly. Furthermore, more variability could result if statistical approaches were used to model shifts in the central tendencies of the variables. The historical period utilized for most variables does not reflect many substantial shifts, and time-series modeling reflects only what occurred in the historical period. As a result, readers should understand that the true range of uncertainty is likely to be larger than indicated in this appendix. Substantial shifts, as predicted by many experts and as seen in prior centuries, are not fully reflected in the current model.
Figure VI.E1 displays the probability distribution of the year-by-year OASDI cost rates (that is, cost as a percentage of taxable payroll). The range of the cost rates widens as the projections move further into the future, which reflects increasing uncertainty. Because there is relatively little variation in income rates across the 5,000 stochastic simulations, the figure includes the income rate only under the intermediate assumptions to indicate the patterns of cash flow for the OASDI program. The two extreme lines in this figure illustrate the range within which future annual cost rates are projected to occur 95 percent of the time (i.e., a 95-percent confidence interval). In other words, the model indicates that there is a 2.5 percent probability that the cost rate in a given year will exceed the upper bound and a 2.5 percent probability that it will fall below the lower bound. Other lines in the figure delineate additional confidence intervals (80‑percent, 60‑percent, 40‑percent, and 20‑percent) around future annual cost rates. The median cost rate for each year is the rate that falls exactly in the middle of possible outcomes for that year. These lines do not represent the results of individual stochastic simulations. Instead, for each given year, they represent the percentile distribution of cost rates based on all stochastic simulations for that year.

Figure VI.E2 presents the simulated probability distribution of the annual trust fund ratios for the combined OASI and DI Trust Funds. The lines in this figure display the median set (50th percentile) of estimated annual trust fund ratios and delineate the 95‑percent, 80‑percent, 60‑percent, 40‑percent, and 20‑percent confidence intervals expected for future annual trust fund ratios. These lines are not the results of individual stochastic simulations. For each given year, they represent the percentile distribution of trust fund ratios based on all stochastic simulations for that year.
Figure VI.E2 shows that the 95‑percent confidence interval for the trust fund depletion year ranges from 2028 to 2044, and there is a 50‑percent probability of trust fund depletion by the end of 2033 (the median depletion year). The median depletion year is the same as the Trustees project under the intermediate assumptions. The figure also shows confidence intervals for the trust fund ratio in each year. For example, the 95‑percent confidence interval for the trust fund ratio in 2025 ranges from 255 to 78 percent of annual cost.

Some of the difference in the ranges of the projected trust fund ratios between two of the methods for illustrating uncertainty (alternative scenarios and stochastic simulations) is due to the different assignment of real interest rates in these two methods. The next section includes an explanation of the different treatments.
This section compares results from two different approaches for determining ranges of uncertainty for trust fund actuarial status. One approach uses results from the low-cost, intermediate, and high-cost alternative scenarios. The other approach uses stochastic distributions of results. Each of these approaches provides insights into uncertainty. Comparison of the results requires an understanding of the differences in the approaches. Two fundamental differences exist between the approach using alternative scenarios and the stochastic approach.
The first fundamental difference relates to presentation of results. Figure VI.E3 shows projected OASDI annual cost rates for the low-cost, intermediate, and high-cost alternatives along with the annual cost rates at the 97.5th percentile, 50th percentile, and 2.5th percentile for the stochastic simulations. While all values on each line for the alternatives are results from a single specified scenario, the values on each stochastic line may be results from different simulations for different years. The one stochastic simulation (from the 5,000 simulations) that yields results closest to a particular percentile in one year may yield results that are distant from that percentile in another year. Thus, the stochastic presentation illustrates distributions of the range of potential results one year at a time, with no direct relationship of the results among years.
Even with this fundamental difference in the presentation of results, figure VI.E3 shows similar results between the range of OASDI cost rates resulting from the alternatives and from the 95-percent confidence interval of stochastic results for years before 2045. After 2045, results for the alternatives show a narrower range. The cost rates for the high-cost alternative are somewhat lower than the stochastic year-by-year results at the 97.5th percentile. The intermediate alternative results show somewhat higher cost rates than the stochastic year-by-year results at the 50th percentile. By far, the largest differences are between the low-cost alternative and the stochastic year-by-year results at the 2.5th percentile. For this comparison, cost rates are substantially higher for the low-cost alternative than for the stochastic year-by-year results at the 2.5th percentile for years after 2045.

The second fundamental difference between the alternatives and the stochastic simulations is the method of assigning values for assumptions in the simulations. For the alternatives, the Trustees assign specific values for key demographic and economic variables. In comparison to the intermediate alternative, almost every value assigned to the high-cost alternative tends to raise estimated program cost and almost every value assigned to the low-cost alternative tends to reduce it. In contrast, the stochastic method randomly assigns values for the key demographic and economic variables in each of the 5,000 independent stochastic simulations. For each of the stochastic simulations, randomly assigned values for the various assumptions may have varying effects on projected cost, with some tending toward higher cost and some tending toward lower cost.
Figure VI.E4 compares the ranges of trust fund (unfunded obligation) ratios for the alternative scenarios and the 95-percent confidence interval of the stochastic simulations. This figure extends figure VI.E2 to show unfunded obligation ratios, expressed as negative values below the zero percent line. Unfunded obligation ratios are the ratio of the unfunded obligation at the beginning of the year to the present value of annual cost for that year. Figure VI.E4 presents a more complete picture of the difference between the results from the three alternative scenarios and the stochastic simulations.

An unfunded obligation, shown as a negative value in this figure, is equivalent to the amount the trust funds would need to have borrowed to date in order to pay all scheduled benefits (on a timely basis) after trust fund asset reserves are depleted. Note that current law does not permit the trust funds to borrow.

After 2045, both trust fund (unfunded obligation) ratios and cost rates are less optimistic for the intermediate scenario than the medians from the stochastic simulation. In addition, both the high-cost trust fund (unfunded obligation) ratios and cost rates are more optimistic than the 2.5th-percentile trust fund (unfunded obligation) ratios and the 97.5th-percentile cost rates, respectively. In sharp contrast, however, the trust fund (unfunded obligation) ratios for the low-cost scenario are more optimistic than the 97.5th-percentile results of the stochastic simulation, even though the cost rates for the low-cost alternative are substantially less optimistic than the 2.5th percentile results of the stochastic simulation.
The treatment of real interest rates between the scenario and stochastic methods provides some insight into the sharp difference between the cost rates and trust fund ratios for the low-cost alternative in relation to the corresponding stochastic results. Projections of trust fund (unfunded obligation) ratios shown in figure VI.E4 require an additional variable not reflected in the cost rates shown in figure VI.E3. This additional variable is the real interest rate. For the alternatives, the Trustees assign higher real interest rates for the low-cost alternative and lower real interest rates for the high-cost alternative. Under the limitations imposed by the law, where the trust funds cannot borrow, a lower real interest rate is relatively pessimistic and thus consistent with the high-cost alternative. However, in order to show the size of the cumulative shortfall of non-interest income relative to scheduled cost (that is, the unfunded obligation) that would not be payable under current law, the Trustees project the cost of scheduled benefits, even after the point at which trust fund reserves become depleted.
In the case of the high-cost alternative, the relatively low assumed real interest rates make trust fund reserves decline faster and deplete sooner and make the unfunded obligation grow more slowly thereafter. For the low-cost alternative, the relatively high assumed real interest rates help maintain trust fund reserves and allow the trust fund reserves to remain close to positive throughout the 75-year projection period.
The stochastic model, however, assigns real interest rates randomly (essentially independent of other variables), yielding rates with very little correlation to the overall “optimism” or “pessimism” of the other variable assignments. The tendency for elevated trust fund ratios for the low-cost alternative resulting from the assignment of high real interest rates is not present in the stochastic results for the corresponding 97.5th percentile, so trust fund reserves decline faster and deplete sooner. This very different assignment of interest rates between the scenario and stochastic methods helps explain the apparent contradiction of having cost rates under the low-cost scenario that are less optimistic, and trust fund ratios under the low-cost scenario that are more optimistic, than the corresponding results of the stochastic simulations. A similar contradiction is not apparent when comparing the high-cost scenario to the corresponding results of the stochastic simulations, because the low real interest rates assigned for the high-cost alternative suppress projected reserves early and also suppress growth in unfunded obligations later in the projection period. Therefore, there is relatively little net effect on the level of unfunded obligations late in the period.
This contrast in results and methods does not mean that either approach to illustrating ranges of uncertainty, alternative scenarios or stochastic simulations, is superior to the other. The ranges are different and explainable.
Table VI.E1 displays long-range actuarial estimates for the combined OASDI program using the two methods of illustrating uncertainty: (1) alternative scenarios and (2) stochastic simulations. The table shows stochastic estimates for the median (50th percentile) and for the 95‑percent and 80‑percent confidence intervals. For comparison, the table shows scenario-based estimates for the intermediate, low-cost, and high-cost assumptions. Each individual stochastic estimate in the table is the level at that percentile from the distribution of the 5,000 simulations. For each given percentile, the values in the table for each long-range actuarial measure are generally from different stochastic simulations.
The median stochastic estimates displayed in table VI.E1 are, in general, slightly more optimistic than the intermediate-alternative scenario-based estimates. The median estimate of the long-range actuarial balance is ‑2.63 percent of taxable payroll, about 0.09 percentage point higher than projected under the intermediate assumptions. The median projected year that cost first exceeds non-interest income (as it did in 2010, 2011, and 2012), and remains in excess of non-interest income throughout the remainder of the long-range period, is 2013. This is the same year as projected under the intermediate assumptions. The median year that asset reserves first become depleted is 2033, also the same as projected under the intermediate assumptions. The median estimates of the annual cost rate for the 75th year of the projection period are 17.54 percent of taxable payroll and 5.80 percent of gross domestic product (GDP). The comparable estimates under the intermediate assumptions are 18.01 percent of payroll and 6.20 percent of GDP.
A comparison of the 95‑percent confidence interval to the range of variation defined by the traditional low-cost and high-cost alternatives follows. For three measures in table VI.E1 (the actuarial balance, the open group unfunded obligation, and the first year asset reserves become depleted), the 95‑percent stochastic confidence interval is narrower than the range defined by the low-cost and high-cost alternatives. In other words, for these measures, the range defined by the low-cost and high-cost alternatives contains the 95‑percent confidence interval of the stochastic modeling projections. For the remaining three measures (the first year cost exceeds non-interest income and remains in excess through 2087, the annual cost in the 75th year as a percent of taxable payroll, and the annual cost in the 75th year as a percent of GDP), one or both of the bounds of the 95‑percent stochastic confidence interval fall outside the range defined by the low-cost and high-cost alternatives.

 Traditional scenario-based model Stochastic model Intermediate Low-cost High-cost Median50thpercentile 80-percentconfidence interval 95-percentconfidence interval 10thpercentile 90thpercentile 2.5thpercentile 97.5thpercentile Actuarial balance -2.72 -0.19 -5.93 -2.63 -4.04 -1.17 -4.84 -0.34 Open group unfunded obligation (in trillions) \$9.6 \$0.2 \$20.6 \$9.4 \$15.2 \$4.2 \$18.8 \$0.9 First projected year cost exceeds non-interest income and remains in excess through 2087a 2013 2013 2013 2013 2013 2013 b First year asset reserves become depletedc 2033 2068 2027 2033 2029 2039 2028 2044 Annual cost in 75th year (percent of taxablepayroll) 18.01 13.15 25.36 17.54 12.95 22.70 10.83 26.05 Annual cost in 75th year (percent of GDP) 6.20 4.93 8.03 5.80 3.70 7.69 2.98 8.86

Cost also exceeded non-interest income in 2010, 2011, and 2012.

For this percentile, cost does not exceed non-interest income in 2087.

For some stochastic simulations, the first year in which trust fund reserves become depleted does not indicate a permanent depletion of reserves.

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